1. Field of the Invention
The invention relates to geological exploration techniques and more specifically to estimation of geologic properties from well logging data.
2. Description of the Related Art
Various instruments applying Nuclear Magnetic Resonance (NMR) imaging technology are useful for measuring certain petrophysical properties of earth formations. NMR well logging instruments typically include a magnet for polarizing nuclei in the earth formations surrounding a wellbore. The polarizing typically occurs along a static magnetic field through use of at least one antenna for transmitting radio frequency (“RF”) energy pulses into the formations. The RF pulses reorient the spin axes of certain nuclei in the earth formations in a predetermined direction. As the spin axes precess and reorient themselves into alignment with the static magnetic field, RF energy is emitted and can be detected by the antenna. The magnitude of the RF energy emitted by the precessing nuclei and the rate at which the magnitude changes are related to certain petrophysical properties of interest in the earth formations.
A typical embodiment of an NMR logging tool for characterization of geologic deposits includes a side-looking or centralized NMR logging tool. Typically, the tool operates using a gradient magnetic field and multiple frequencies. One example of such a tool is the MX ExplorerSM provided by Baker Hughes, Inc. of Houston Tex. (referred to as the “MREX tool,” the “logging tool” or simply as the “tool” herein).
There are several principal operating parameters in NMR well logging which should be optimized for efficient operation of an NMR well logging instrument. These parameters include the logging speed (speed of motion of the instrument along the wellbore), the average and the peak power supplied to the instrument and transmitted as RF pulses, and the signal-to-noise ratio (“SNR”). Other parameters of interest include the vertical resolution of the instrument and the radial depth of investigation of the measurements made by the instrument within the formations surrounding the wellbore.
Physical parameters of particular interest to wellbore operators are the fractional volume of pore spaces in the earth formations (“porosity”), the texture of the rock and connectivity of the pore spaces, and the nature of the fluids contained in the pore spaces. In petroleum bearing earth formations, the pore spaces will typically contain some fractional volume of water and some fractional volume of hydrocarbons. Since hydrocarbons generally have different NMR relaxation properties than water, various NMR relaxometry techniques have been developed to qualitatively determine the nature of the fluids present in certain earth formations.
One method, for example, enables discriminating between gas and oil, and light oil and water. This method includes performing NMR spin-echo experiments using two different “wait times”, Tw. The wait time Tw is the delay between individual Carr-Purcell-Meiboom-Gill (“CPMG”) spin echo measurement sequences. See S. Meiboom et al, Rev. of Sci. Instr. v. 29, p. 6881 (1958). Another technique, described in U.S. Pat. No. 5,498,960 issued to Vinegar et al, uses two different inter-echo spacing times, TE, for CPMG sequences measured in a gradient magnetic field. Typically, the inter-echo spacing is the time between rephasing radio frequency (RF) energy pulses applied to the logging instrument's antenna to “rephase” precessing nuclei which are influenced by the NMR survey. The rephasing RF pulses result in the “spin echoes” whose amplitude is measured. Gas, oil and water generally have different self-diffusivities, and these differences will be reflected in differences in the apparent transverse relaxation time T2 calculated for an earth formation between CPMG sequences measured using different values of TE. The technique described in the Vinegar et al '960 patent for discriminating types of fluids in pore spaces of earth formations typically uses two values of TE.
Another physical property of particular interest is the viscosity of any oil which may be present in the pore spaces of the earth formation. A relationship between an intrinsic transverse relaxation time, T2int, for oil with respect to its viscosity, η is provided:
                                          T                          2              ⁢                                                          ⁢              int                                =                                    1.2              ⁢                              T                K                                                    298              ⁢                              η                x                                                    ;                            (        1        )            where TK represents the absolute temperature (in ° K) of the oil and x represents an empirical fit factor, typically about equal to unity. A difficulty in determining oil viscosity η using this relationship is that it requires determining the intrinsic transverse relaxation time T2int. For NMR logging instruments that use a gradient static magnetic field, the transverse relaxation time T2 calculated from spin-echo amplitude measurements is affected by a self-diffusion effect T2D. An apparent transverse relaxation time T2 calculated from the spin echo amplitudes is related to the intrinsic transverse relaxation time T2int in the following manner:
                                          1                          T              2                                =                                    1                              T                                  2                  ⁢                                                                          ⁢                  int                                                      +                          1                              T                                  2                  ⁢                  D                                                                    ;                            (        2        )            where the self-diffusion effect T2D can be determined by the expression:
                                          1                          T                              2                ⁢                D                                              =                                                    D                ⁡                                  (                                      γ                    *                    TE                    *                                          G                      Z                                                        )                                            2                        12                          ;                            (        3        )            where an inter-echo time TE is generally selected by the system operator and has a known value; D represents a diffusivity of the media; the gyromagnetic ratio γ is unique for each nuclear isotope; and the magnetic field gradient GZ, is dependent upon a frequency (f) and includes an internal gradient component Gint and an external gradient component GMREX. The magnitude of the static magnetic field, B0, in which the CPMG sequences are actually measured, is therefore controlled by selection of a frequency for the RF pulses. Since the spatial distribution of the static magnetic field amplitude and gradient magnitude are known, the gradient of the static magnetic field in the NMR excitation volume will also be known for any selected RF excitation frequency. The actual magnetic field gradient within the pore spaces of the earth formation may not be known, however, since the field gradients internal to the pore spaces depend on differences in magnetic susceptibility between the formation solids (“matrix”) and the fluid in the pore spaces, as well as the amplitude of the static magnetic field. See for example, U.S. Pat. No. 5,698,979 issued to Taicher et al.
Determination of the internal gradient Gint(f) of the static magnetic field B0 is essential for accurate material typing using diffusion-based NMR techniques. Since the internal gradient Gint(f) is related to the pore mineralogy and pore geometry, the internal gradient Gint(f) may also be used to obtain additional information about properties of the porous rock.
The internal gradient Gint(f) in porous media arises from differences in the magnetic properties between minerals in the formation matrix and material (e.g., fluid) in pore spaces of the formation. Mathematically, the internal gradient Gint(f) is described as:
                                          G            int                    ∝                                    Δχ              ·                              B                0                                      r                          ;                            (        4        )            where 1/r represents the curvature of a pore within the formation, where Δχ represents magnetic properties in the formation (also referred to as a “susceptibility difference” between the matrix and the fluid) and B0 represents an applied static magnetic field. Although Δχ is theoretically a dispersive quantity, for the low-frequency range of NMR logging interest, it can be regarded as typically being frequency independent. The internal gradient Gint is therefore dependent upon the static-field B0. Consequently, for a logging tool that makes use of multiple frequencies to generate a gradient magnetic field, the internal gradient Gint is also frequency dependent.
The effective gradient along the field direction Gint(f) may therefore be described as:
                                          G            ⁡                          (              f              )                                =                                                                      G                                      z                    ,                    int                                                  ⁡                                  (                  f                  )                                            +                                                G                  MREX                                ⁡                                  (                  f                  )                                                      =                                          a                ·                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      ·                      Δχ                                                                            γ                    ·                    r                                                              +                              b                ·                                  f                  c                                                                    ;                            (        5        )            Where G represents a radiofrequency (RF) field gradient strength; a is substantially equal to unity, while b and c are two coefficients dependent on aspects of the NMR logging instrument. For an MREX logging tool, b is approximately 40 and c is approximately 1.5. This function includes two operands, where the first operand Gz,int(f) represents the internal magnetic field gradient and GMREX(f) represents the logging tool magnetic field gradient (also referred to as an “external magnetic field gradient”).
Eq. (5) shows that both the internal gradient Gint(f) and the tool gradient GMREX(f) are frequency dependent. However, these dependencies are different. The internal gradient Gz,int(f) is linearly proportional to f, but the tool gradient GMREX(f) generally depends upon frequency more than linearity. In the prior art, typical diffusion based NMR fluid typing techniques acquire multiple G(f)*TE echo trains for hydrocarbon typing where G(f) has always been simplified to the tool gradient GMREX(f) and a contribution by the internal gradient Gint(f) has been discounted. Inherently, this assumption causes inaccuracies in results.
What is needed is a technique for accurately determining the internal magnetic field gradient Gz,int(f) of the earth formation for a given NMR well logging tool and operating frequency, which will in turn provide for accurate typing of materials (fluids as well as minerals) of formations using diffusion based NMR techniques.